Modelling and simulation of transportation system effectiveness to reduce traffic congestion: a system dynamics framework

ABSTRACT

This paper is designed to evaluate and improve the effectiveness of transportation systems and reduce traffic congestion through the use of simulation models and scenario development. A system dynamics framework is used to test and evaluate the alternatives of future strategies for the city of Surabaya, Indonesia. Some factors affecting the effectiveness of transport systems include operational effectiveness and service effectiveness, as well as uncertainty. To improve the effectiveness of transportation systems, several strategies can be implemented, such as subsidizing public transportation, increasing the cost of private vehicle parking fees, raising taxes on private vehicles, and reducing delays in public transportation through scenario development. Scenario results show that, by pursuing these strategies, effectiveness could be improved by 80% as the impact of the increase in operational and service effectiveness, helping to mitigate traffic congestion. Congestion could be reduced to 70% (on average) due to the decrease in daily traffic.     

A bi-level model for GHG emission charge based on a continuous distribution of travelers’ value of time (VOT)

Transportation is an important source of greenhouse gas (GHG) emissions. In this paper, we develop a bi-level model for GHG emission charge based on continuous distribution of the value of time (VOT) for travelers. In the bi-level model framework, a policy maker (as the leader) seeks an optimal emission charge scheme, with tolls differentiated across travel modes (e.g., bus, motorcycles, and cars), to achieve a given GHG reduction target by shifting the proportions of travelers taking different modes. In response, travelers (as followers) will adjust their travel modes to minimize their total travel cost. The resulting mode shift, hence the outcome of the emission charge policy, depends on travelers’ VOT distribution. For the solution of the bi-level model, we integrate a differential evolution algorithm for the upper level and the “all or nothing” traffic assignment for the lower level. Numerical results from our analysis suggest important policy implications: (1) in setting the optimal GHG emission charge scheme for the design of transportation GHG emission reduction targets, policy makers need to be equipped with rigorous understanding of travelers’ VOT distribution and the tradeoffs between emission reduction and system efficiency; and (2) the optimal emission charge scheme in a city depends significantly on the average value of travelers’ VOT distribution—the optimal emission charge can be designed and implemented in consistency with rational travel flows. Further sensitivity analysis considering various GHG reduction targets and different VOT distributions indicate that plausible emission toll schemes that encourage travelers to choose greener transportation modes can be explored as an efficient policy instrument for both transportation network performance improvement and GHG reduction.     

Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains

This paper proposes a methodology to generate a robust logistics plan that can mitigate demand uncertainty in humanitarian relief supply chains. More specifically, we apply robust optimization (RO) for dynamically assigning emergency response and evacuation traffic flow problems with time dependent demand uncertainty. This paper studies a Cell Transmission Model (CTM) based system optimum dynamic traffic assignment model. We adopt a min–max criterion and apply an extension of the RO method adjusted to dynamic optimization problems, an affinely adjustable robust counterpart (AARC) approach. Simulation experiments show that the AARC solution provides excellent results when compared to deterministic solution and sampling based stochastic programming solution. General insights of RO and transportation that may have wider applicability in humanitarian relief supply chains are provided.     

Heterogeneous sensor location model for path reconstruction

A new traffic sensor location problem is developed and solved by strategically placing both passive and active sensors in a transportation network for path reconstruction. Passive sensors simply count vehicles, while active sensors can recognize vehicle plates but are more expensive. We developed a two-stage heterogeneous sensor location model to determine the most cost-effective strategies for sensor deployment. The first stage of the model adopts the path reconstruction model defined by Castillo et al. (2008b) to determine the optimal locations of active sensors in the network. In the second stage, an algebraic framework is developed to strategically replace active sensors so that the total installation cost can be reduced while maintaining path flow observation quality. Within the algebraic framework, a scalar product operator is introduced to calculate path flows. An extension matrix is generated and used to determine if a replacement scheme is able to reconstruct all path flows. A graph model is then constructed to determine feasible replacement schemes. The problem of finding the optimal replacement scheme is addressed by utilizing the theory of maximum clique to obtain the upper bound of the number of replaced sensors and then revising this upper bound to generate the optimal replacement scheme. A polynomial-time algorithm is proposed to solve the maximum clique problem, and the optimal replacement scheme can be obtained accordingly. Three numerical experiments show that our proposed two-stage method can reduce the total costs of transportation surveillance systems without affecting the system monitor quality. The locations of the active sensors play a more critical role than the locations of the passive sensors in the number of reconstructed paths.     

Boundedly rational user equilibria (BRUE): Mathematical formulation and solution sets

Boundedly rational user equilibria (BRUE) represent traffic flow distribution patterns where travellers can take any route whose travel cost is within an ‘indifference band’ of the shortest path cost. Those traffic flow patterns satisfying the above condition constitute a set, named the BRUE solution set. It is important to obtain all the BRUE flow patterns, because it can help predict the variation of the link flow pattern in a traffic network under the boundedly rational behavior assumption. However, the methodology of constructing the BRUE set has been lacking in the established literature. This paper fills the gap by constructing the BRUE solution set on traffic networks with fixed demands. After defining ε-BRUE, where ε is the indifference band for the perceived travel cost, we formulate the ε-BRUE problem as a nonlinear complementarity problem (NCP), so that a BRUE solution can be obtained by solving a BRUE–NCP formulation. To obtain the BRUE solution set encompassing all BRUE flow patterns, we propose a methodology of generating acceptable path set which may be utilized under the boundedly rational behavior assumption. We show that with the increase of the indifference band, the acceptable path set that contains boundedly rational equilibrium flows will be augmented, and the critical values of indifference band to augment these path sets can be identified by solving a family of mathematical programs with equilibrium constraints (MPEC) sequentially. The BRUE solution set can then be obtained by assigning all traffic demands to the acceptable path set. Various numerical examples are given to illustrate our findings.     

Robust intermodal hub location under polyhedral demand uncertainty

In this study, we consider the robust uncapacitated multiple allocation p-hub median problem under polyhedral demand uncertainty. We model the demand uncertainty in two different ways. The hose model assumes that the only available information is the upper limit on the total flow adjacent at each node, while the hybrid model additionally imposes lower and upper bounds on each pairwise demand. We propose linear mixed integer programming formulations using a minmax criteria and devise two Benders decomposition based exact solution algorithms in order to solve large-scale problems. We report the results of our computational experiments on the effect of incorporating uncertainty and on the performance of our exact approaches.     

Determining structural route components from GPS traces

Analysis of GPS traces shows that people often do not use the least cost path through the transportation network while making trips. This leads to the question which structural path characteristics can be used to construct realistic route choice sets for use in traffic simulation models. In this paper, we investigate the hypothesis that, for utilitarian trips, the route between origin and destination consists of a small number of concatenated least cost paths. The hypothesis is verified by analyzing routes extracted from large sets of recorded GPS traces which constitute revealed preference information. Trips have been extracted from the traces and for each trip the path in the transportation network is determined by map matching. This is followed by a path decomposition phase for which the algorithm constitutes the first contribution of this paper. There are multiple ways to split a given path in a directed graph into a minimal number of subpaths of minimal cost. By calculating two specific path splittings, it is possible to identify subsets of the vertices (splitVertexSuites) that can be used to generate every possible minimum path splitting by taking one vertex from each such subset. As a second contribution, we show how the extracted information is used in microscopic travel simulation. The distribution for the size of the minimum decomposition, extracted from the GPS traces, can be used in constrained enumeration methods for route choice set generation. The sets of vertices that can act as boundary vertices separating consecutive route parts contain way points (landmarks) having a particular meaning to their user. The paper explains the theoretical aspects of route splitting as well as the process to extract splitVertexSuites from big data. It reports statistical distributions extracted from sets of GPS traces for both multimodal person movements and unimodal car trips.     

On some traffic equilibrium theory paradoxes

We consider the asymmetric equilibrium problem with fixed demands in a transportation network where the travel cost on each link may depend on the flow on this as well as other links of the network and we study how the travellers' cost is affected by changes in the travel demand or addition of new routes. Assuming that the travel cost functions are strongly monotone, we derive formulas which express, under certain conditions, how a change in travel demand associated with a particular origin-destination (O / D) pair will affect the travelers' cost for any O / D pair. We then use these formulas to show that an increase in the travel demand associated with a particular O / D pair (all other remaining fixed) always results in an increase in the travelers' cost on that O / D pair, however, the travelers' cost on other O / D pairs may decrease. We then derive formulas yielding, under certain conditions, the change in travelers' cost on every O / D pair induced by the addition of a new path. These can be used to determine, whether Braess' paradox occurs in the network. We then show that when a new path is added, the travelers' cost associated with the particular O / D pair joined by this path will decrease (hence Braess' paradox does not occur) if a test matrix is positive semidefinite.     

Distribution-free travel time reliability assessment with probability inequalities

An assumption that pervades the current transportation system reliability assessment literature is that probability distributions of the sources of uncertainty are known explicitly. However, this distribution may be unavailable (inaccurate) in reality as we may have no (insufficient) data to calibrate the distribution. In this paper we relax this assumption and present a new method to assess travel time reliability that is distribution-free in the sense that the methodology only requires that the first N moments (where N is a user-specified positive integer) of the travel time to be known and that the travel times reside in a set of bounded and known intervals. Because of our modeling approach, all sources of uncertainty are automatically accounted for, as long as they are statistically independent. Instead of deriving exact probabilities on travel times exceeding certain thresholds via computationally intensive methods, we develop semi-analytical probability inequalities to quickly (i.e. within a fraction of a second) obtain upper bounds on the desired probability. Numerical experiments suggest that the inclusion of higher order moments can potentially significantly improve the bounds. The case study also demonstrates that the derived bounds are nontrivial for a large range of travel time values.     

Cost scaling based successive approximation algorithm for the traffic assignment problem

This paper presents a cost scaling based successive approximation algorithm, called ε-BA (ε-optimal bush algorithm), to solve the user equilibrium traffic assignment problem by successively refining ε-optimal flows. As ε reduces to zero, the user equilibrium solution is reached. The proposed method is a variant of bush-based algorithms, and also a variant of the min-mean cycle algorithm to solve the min-cost flow by successive approximation. In ε-BA, the restricted master problem, implying traffic equilibration restricted on a bush, is solved to ε-optimality by cost scaling before bush reconstruction. We show that ε-BA can reduce the number of flow operations substantially in contrast to Dial’s Algorithm B, as the former operates flows on a set of deliberately selected cycles whose mean values are sufficiently small. Further, the bushes can be constructed effectively even if the restricted master problem is not solved to a high level of convergence, by leveraging the ε-optimality condition. As a result, the algorithm can solve a highly precise solution with faster convergence on large-scale networks compared to our implementation of Dial’s Algorithm B.     

Green supply chain network design to reduce carbon emissions

We consider a supply chain network design problem that takes CO₂ emissions into account. Emission costs are considered alongside fixed and variable location and production costs. The relationship between CO₂ emissions and vehicle weight is modeled using a concave function leading to a concave minimization problem. As the direct solution of the resulting model is not possible, Lagrangian relaxation is used to decompose the problem into a capacitated facility location problem with single sourcing and a concave knapsack problem that can be solved easily. A Lagrangian heuristic based on the solution of the subproblem is proposed. When evaluated on a number of problems with varying capacity and cost characteristics, the proposed algorithm achieves solutions within 1% of the optimal. The test results indicate that considering emission costs can change the optimal configuration of the supply chain, confirming that emission costs should be considered when designing supply chains in jurisdictions with carbon costs.     

A two-dimensional framework for the understanding of transportation planning models

This article puts forward the view that, for each transportation planning or management problem, there is a particular way to simultaneously define the multiple levels of procedures useful for the problem and set it in its proper perspective, the latter essentially by the identification of what is exogenous and endogenous to the problem at hand. The joint determination of these levels and of the exogenous/endogenous mix defines the two-dimensional frame of each problem. To develop our view, we extend our previous conceptual framework to include, in the first dimension, an activity location procedure, and to distinguish, in the second dimension, between operational, tactical, and strategic perspectives. We conclude by relativising the use of solution techniques by making them ancillary to the situation planning requirements.     

Just-in-time delivery for green fleets: A feedback control approach

With increasing attention being paid to greenhouse gas (GHG) emissions, the transportation industry has become an important focus of approaches to reduce GHG emissions, especially carbon dioxide equivalent (CO₂e) emissions. In this competitive industry, of course, any new emissions reduction technique must be economically attractive and contribute to good operational performance. In this paper, a continuous-variable feedback control algorithm called GEET (Greening via Energy and Emissions in Transportation) is developed; customer deliveries are assigned to a fleet of vehicles with the objective function of Just-in-Time (JIT) delivery and fuel performance metrics akin to the vehicle routing problem with soft time windows (VRPSTW). GEET simultaneously determines vehicle routing and sets cruising speeds that can be either fixed for the entire trip or varied dynamically based on anticipated performance. Dynamic models for controlling vehicle cruising speed and departure times are proposed, and the impact of cruising speed on JIT performance and fuel performance are evaluated. Allowing GEET to vary cruising speed is found to produce an average of 12.0–16.0% better performance in fuel cost, and −36.0% to +16.0% discrepancy in the overall transportation cost as compared to the Adaptive Large Neighborhood Search (ALNS) heuristic for a set of benchmark problems. GEET offers the advantage of extremely fast computational times, which is a substantial strength, especially in a dynamic transportation environment.     

Solving the bicriterion routing and scheduling problem for hazardous materials distribution

Hazardous materials routing and scheduling decisions involve the determination of the minimum cost and/or risk routes for servicing the demand of a given set of customers. This paper addresses the bicriterion routing and scheduling problem arising in hazardous materials distribution planning. Under the assumption that the cost and risk attributes of each arc of the underlying transportation network are time-dependent, the proposed routing and scheduling problem pertains to the determination of the non-dominated time-dependent paths for servicing a given and fixed sequence of customers (intermediate stops) within specified time windows. Due to the heavy computational burden for solving this bicriterion problem, an alternative algorithm is proposed that determines the k-shortest time-dependent paths. Moreover an algorithm is provided for solving the bicriterion problem. The proximity of the solutions of the k-shortest time-dependent path problem with the non-dominated solutions is assessed on a set of problems developed by the authors.     

Robust network sensor location for complete link flow observability under uncertainty

The link observability problem is to identify the minimum set of links to be installed with sensors that allow the full determination of flows on all the unobserved links. Inevitably, the observed link flows are subject to measurement errors, which will accumulate and propagate in the inference of the unobserved link flows, leading to uncertainty in the inference process. In this paper, we develop a robust network sensor location model for complete link flow observability, while considering the propagation of measurement errors in the link flow inference. Our model development relies on two observations: (1) multiple sensor location schemes exist for the complete inference of the unobserved link flows, and different schemes can have different accumulated variances of the inferred flows as propagated from the measurement errors. (2) Fewer unobserved links involved in the nodal flow conservation equations will have a lower chance of accumulating measurement errors, and hence a lower uncertainty in the inferred link flows. These observations motivate a new way to formulate the sensor location problem. Mathematically, we formulate the problem as min–max and min–sum binary integer linear programs. The objective function minimizes the largest or cumulative number of unobserved links connected to each node, which reduces the chance of incurring higher variances in the inference process. Computationally, the resultant binary integer linear program permits the use of a number of commercial software packages for its globally optimal solution. Furthermore, considering the non-uniqueness of the minimum set of observed links for complete link flow observability, the optimization programs also consider a secondary criterion for selecting the sensor location scheme with the minimum accumulated uncertainty of the complete link flow inference.     

System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network

Thanks to its high dimensionality and a usually non-convex constraint set, system optimal dynamic traffic assignment remains one of the most challenging problems in transportation research. This paper identifies two fundamental properties of the problem and uses them to design an efficient solution procedure. We first show that the non-convexity of the problem can be circumvented by first solving a relaxed problem and then applying a traffic holding elimination procedure to obtain the solution(s) of the original problem. To efficiently solve the relaxed problem, we explore the relationship between the relaxed problems based on different traffic flow models (PQ, SQ, CTM) and a minimal cost flow (MCF) problem for a special space-expansion network. It is shown that all the four problem formulations produce the same minimal system cost and share one common solution which does not involve inside queues in the network. Efficient solution algorithms such as the network simplex method can be applied to solve the MCF problem and identify such an optimal traffic pattern. Numerical examples are also presented to demonstrate the efficiency of the proposed solution procedure.     

Design framework of large-scale one-way electric vehicle sharing systems: A continuum approximation model

This paper proposes a Continuum Approximation (CA) model for design of a one-way Electrical Vehicle (EV) sharing system that serves a metropolitan area. This model determines the optimal EV sharing station locations and the corresponding EV fleet sizes to minimize the comprehensive system cost, including station construction investment, vehicle charging, transportation and vehicle balancing, under stochastic and dynamic trip demands. This is a very complex problem due to the NP-hard nature of location design, the large number of individual users, and the stochasticity and dynamics of generated trips. Further, the considerable charging time required by EVs distinguishes this problem from traditional car sharing problems where a vehicle is immediately available for pickup after being dropped at a station. We find that the CA approach can overcome these modeling challenges by decomposing the studied area into a number of small neighborhoods that each can be approximated by an Infinite Homogeneous Plane (IHP). We find that the system cost of an IHP is a unimodal function of the station service area size and can be efficiently solved in a sub-linear time by the bisection algorithm. Then integrating the solutions of all IHPs yields an approximate solution to the original heterogeneous area. With numerical experiments, we show that the CA solution is able to estimate the total system cost of the discrete counterpart solution efficiently with good accuracy, even for large-scale heterogeneous problems. This implies that the proposed CA approach is capable of providing a near-optimum solution to the comprehensive design of a practical large-scale EV sharing system. With this model, we also conduct sensitivity analysis to reveal insights into how cost components and system design vary with key parameter values. As far as the author’s knowledge, this study is the first work that addresses design of an EV sharing system considering both longer-term location and fleet size planning and daily vehicle operations. The proposed CA model also extends the CA methodology literature from traditional location problems with stationary demand, single-facility based service to EV sharing problems considering dynamic demands, OD trips, and nonlinear vehicle charging times.     

Transportation carbon dioxide emissions by built environment and family lifecycle: Case study of the Osaka metropolitan area

How a city grows and changes, along with where people choose to live likely affects travel behavior, and thus the amount of transportation CO₂ emissions that they produce. People generally go through different stages in their life, and different travel needs are associated with each. The impact of the built environment may vary depending on the lifecycle stage, and the years spent at each stage will differ. A family with children may last for twenty to thirty years, while the time spent without dependents might be short in comparison. Over a family’s lifecycle, how big of a difference might the built environment, through household location choice, have on the amount of transportation CO₂ emissions produced? From a climate change perspective, how significant is residential location on the CO₂ produced by transportation use? This paper uses data from the Osaka metropolitan area to compare the direct transportation CO₂ emissions produced over a family’s lifecycle across five different built environments to determine whether any are sustainable and which lifecycle stage has the greatest overall emissions. This understanding would enable the design of a targeted policy based on household lifecycle to reduce overall transportation CO₂ of individuals throughout one’s lifecycle. The yearly average per-capita family lifetime transportation CO₂ emissions were 0.25, 0.35, 0.58, 0.78, and 0.79 metric tonnes for the commercial, mixed-commercial, mixed-residential, autonomous, and rural areas respectively. The results show that only the commercial and mixed-commercial areas were considered to be sustainable from a climate change and transportation perspective.     

A math-heuristic algorithm for the integrated air service recovery

A sophisticated flight schedule might be easily disrupted due to adverse weather, aircraft mechanical failures, crew absences, etc. Airlines incur huge costs stemming from such flight schedule disruptions in addition to the serious inconveniences experienced by passengers. Therefore, an efficient recovery solution that simultaneously decreases an airline's recovery cost while simultaneously mitigating passenger dissatisfaction is of great importance to the airline industry. In this paper, we study the integrated airline service recovery problem in which the aircraft and passenger schedule recovery problems are simultaneously addressed, with the objective of minimizing aircraft recovery and operating costs, passenger itinerary delay cost, and passenger itinerary cancellation cost.Recognizing the inherent difficulty in modeling the integrated airline service recovery problem within a single formulation (due to its huge solution space and quick response requirement), we propose a three-stage sequential math-heuristic framework to efficiently solve this problem, wherein the flight schedules and aircraft rotations are recovered in the first stage, Then, a flight rescheduling problem and passenger schedule recovery problems are iteratively solved in the next two stages. Time-space network flow representations, along with mixed-integer programming formulations, and algorithms that take advantages of the underlying problem structures, are proposed for each of three stages. This algorithm was tested on realistic data provided by the ROADEF 2009 challenge and the computational results reveal that our algorithm generated the best solution in nearly 72% of the test instances, and a near-optimal solution was achieved in the remaining instances within an acceptable timeframe. Furthermore, we also ran additional computational runs to explore the underlying characteristics of the proposed algorithm, and the recorded insights can serve as a useful guide during practical implementations of this algorithm.     

Two-phase stochastic program for transit network design under demand uncertainty

This paper develops a reliability-based formulation for rapid transit network design under demand uncertainty. We use the notion of service reliability to confine the stochastic demand into a bounded uncertainty set that the rapid transit network is designed to cover. To evaluate the outcome of the service reliability chosen, flexible services are introduced to carry the demand overflow that exceeds the capacity of the rapid transit network such designed. A two-phase stochastic program is formulated, in which the transit line alignments and frequencies are determined in phase 1 for a specified level of service reliability; whereas in phase 2, flexible services are determined depending on the demand realization to capture the cost of demand overflow. Then the service reliability is optimized to minimize the combined rapid transit network cost obtained in phase 1, and the flexible services cost and passenger cost obtained in phase 2. The transit line alignments and passenger flows are studied under the principles of system optimal (SO) and user equilibrium (UE). We then develop a two-phase solution algorithm that combines the gradient method and neighborhood search and apply it to a series of networks. The results demonstrate the advantages of utilizing the two-phase formulation to determine the service reliability as compared with the traditional robust formulation that pre-specifies a robustness level.